Police leaders, including Boston Police Commissioner William Evans, rallied at the State House Tuesday in opposition to the Senate plan.

“I side with the police chiefs who were here yesterday and the law-enforcement officials, that the House version is the stronger of the two,’’ Patrick told reporters, according to a transcript of his comments released by his office.

Under current law, police chiefs must give people who pass a background check and meet other basic criteria a firearms identification card, which allows them to buy shotguns and rifles. But for handguns, police chiefs have discretion on whether to issue a license to carry and can deny one if they deem an applicant unsuitable. The disputed part of the bill would give chiefs the same discretion they currently have on issuing handgun licenses and apply it to rifles and shotguns.

Patrick said he hopes the version finally approved by leaders of both houses in the Legislature will “come out closer to the House version.’’

Asked if he would sign the Senate version, the governor replied that it was too soon to say. “You know I can express my preference right now, but you know how the sausage is made,” he said. “We’ll see what we get in the end.’’

With the issue raised by police set aside, Patrick said the measure overall “represents a compromise and a pretty constructive one . . . I think in either case we will have a bill that is a step forward.’’